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Transverse lines to surfaces over finite fieldsMar 21 2019We prove that if $S$ is a smooth reflexive surface in $\mathbb{P}^3$ defined over a finite field $\mathbb{F}_q$, then there exists an $\mathbb{F}_q$-line meeting $S$ transversely provided that $q\geq c\operatorname{deg}(S)$, where $c=\frac{3+\sqrt{17}}{4}\approx ... More

Transverse lines to surfaces over finite fieldsMar 21 2019Apr 08 2019We prove that if $S$ is a smooth reflexive surface in $\mathbb{P}^3$ defined over a finite field $\mathbb{F}_q$, then there exists an $\mathbb{F}_q$-line meeting $S$ transversely provided that $q\geq c\operatorname{deg}(S)$, where $c=\frac{3+\sqrt{17}}{4}\approx ... More

AI Oriented Large-Scale Video Management for Smart City: Technologies, Standards and BeyondDec 05 2017Deep learning has achieved substantial success in a series of tasks in computer vision. Intelligent video analysis, which can be broadly applied to video surveillance in various smart city applications, can also be driven by such powerful deep learning ... More

Quantum Information Meets Quantum Matter -- From Quantum Entanglement to Topological Phase in Many-Body SystemsAug 11 2015Feb 23 2018This is the draft version of a textbook, which aims to introduce the quantum information science viewpoints on condensed matter physics to graduate students in physics (or interested researchers). We keep the writing in a self-consistent way, requiring ... More

Designing Fully Distributed Consensus Protocols for Linear Multi-agent Systems with Directed GraphsDec 28 2013Aug 20 2014This paper addresses the distributed consensus protocol design problem for multi-agent systems with general linear dynamics and directed communication graphs. Existing works usually design consensus protocols using the smallest real part of the nonzero ... More

Known-class Aware Self-ensemble for Open Set Domain AdaptationMay 03 2019Existing domain adaptation methods generally assume different domains have the identical label space, which is quite restrict for real-world applications. In this paper, we focus on a more realistic and challenging case of open set domain adaptation. ... More

Stable Soliton Excitations in Modulational Instability Regime with the Fourth-order EffectsNov 02 2016We study the correspondence between modulational instability and types of fundamental nonlinear excitation in a nonlinear fiber with both third-order and fourth-order effects. Some stable soliton excitations are obtained in modulational instability regime, ... More

Zero-Energy Modes on Superconducting Bismuth Islands Deposited on Fe(Te,Se)May 14 2019Topological superconductivity is one of the frontier research directions in condensed matter physics. One of the unique elementary excitations in topological superconducting state is the Majorana fermion (mode) which is its own antiparticle and obeys ... More

A Constructive Algorithm to Prove P=NPJul 31 2012After reducing the undirected Hamiltonian cycle problem into the TSP problem with cost 0 or 1, we developed an effective algorithm to compute the optimal tour of the transformed TSP. Our algorithm is described as a growth process: initially, constructing ... More

Symmetric and asymmetric optical multi-peak solitons on a continuous wave background in the femtosecond regimeMar 15 2016We study symmetric and asymmetric optical multi-peak solitons on a continuous wave background in the femtosecond regime of a single-mode fiber. Key characteristics of such multi-peak solitons, as the formation mechanism, propagation stability, and shape-changing ... More

Realization of room-temperature ferromagnetic semiconducting state in graphene monolayerApr 20 2017Nov 22 2017Room-temperature ferromagnetic semiconductor is vital in nonvolatile digital circuits and it can provide an idea system where we can make use of both charge and spin of electrons. However, seeking room-temperature ferromagnetic semiconductors is still ... More

Structural instabilities and mechanical properties of U$_2$Mo from first principles calculationsNov 03 2014We perform detailed first principles calculations of the structural parameters at zero pressure and high pressure, the elastic properties, phonon dispersion relation, and ideal strengths of U$_2$Mo with $C11_b$ structure. In contrast to previous theoretical ... More

Bulk Matters on Symmetric and Asymmetric de Sitter Thick BranesJan 07 2009Feb 03 2009An asymmetric thick domain wall solution with de Sitter ($dS$) expansion in five dimensions can be constructed from a symmetric one by using a same scalar (kink) with different potentials. In this paper, by presenting the mass-independent potentials of ... More

Localization and Mass Spectrum of Matters on Weyl Thick BranesMar 02 2008Aug 12 2008In this paper, we study localization and mass spectrum of various matter fields on a family of thick brane configurations in a pure geometric Weyl integrable 5-dimensional space time, a non-Riemannian modification of 5-dimensional Kaluza--Klein (KK) theory. ... More

Magnetic Ordering Induced Giant Optical Property Change in Tetragonal BiFeO3Aug 17 2015Magnetic ordering, as one of the most important characteristics in magnetic materials, could have significant influence on the band structure, spin dependent transport, and other important properties of materials. Its measurement, especially for the case ... More

Intelligent Power Control for Spectrum Sharing in Cognitive Radios: A Deep Reinforcement Learning ApproachDec 20 2017Apr 08 2018We consider the problem of spectrum sharing in a cognitive radio system consisting of a primary user and a secondary user. The primary user and the secondary user work in a non-cooperative manner. Specifically, the primary user is assumed to update its ... More

Inner Structure of Spin^{c}(4) Gauge Potential on 4-Dimensional ManifoldsJan 28 2007Nov 02 2008The decomposition of $Spin^{c}(4)$ gauge potential in terms of the Dirac 4% -spinor is investigated, where an important characterizing equation $\Delta A_{\mu}=-\lambda A_{\mu}$ has been discovered. Here $\lambda $ is the vacuum expectation value of the ... More

Glass formation in a mixture of hard disks and hard ellipsesMay 26 2015We present an event-driven molecular dynamics study of glass formation in two-dimensional binary mixtures composed of hard disks and hard ellipses, where both types of particles have the same area. We demonstrate that characteristic glass-formation behavior ... More

Precision study on $ZZγ$ production including $Z$-boson leptonic decays at the ILCDec 07 2015Mar 15 2016We report on the precision predictions for the $e^+e^-\to ZZ\gamma$ process including $Z$-boson leptonic decays at the ILC in the standard model (SM). The calculation includes the full next-to-leading (NLO) electroweak (EW) corrections and high order ... More

QCD correction to gluino decay to $t\bar{t}\tildeχ^0_1$ in the MSSMJul 25 2012Aug 27 2012We calculate the complete next-to-leading order QCD corrections to the three-body decay of gluino into top-pair associated with a lightest neutralino in the minimal supersymmetric standard model. We obtain that the LO and NLO QCD corrected decay widths ... More

Compact Descriptors for Video Analysis: the Emerging MPEG StandardApr 26 2017This paper provides an overview of the on-going compact descriptors for video analysis standard (CDVA) from the ISO/IEC moving pictures experts group (MPEG). MPEG-CDVA targets at defining a standardized bitstream syntax to enable interoperability in the ... More

Electrically tunable multiple Dirac cones in thin films of (LaO)2(SbSe2)2 family of materialsSep 12 2014Oct 20 2015Two-dimensional Dirac physics has aroused great interests in condensed matter physics ever since the discovery of graphene and topological insulators due to its importance in both fundamental physics and device applications. The ability to control the ... More

Heterogeneous information network model for equipment-standard systemMar 07 2017Entity information network is used to describe structural relationships between entities. Taking advantage of its extension and heterogeneity, entity information network is more and more widely applied to relationship modeling. Recent years, lots of researches ... More

Deterministic Role of Concentration Surplus of Cation Vacancy over Anion Vacancy in Bipolar Memristive NiOJan 29 2017Migration of oxygen vacancies has been proposed to play an important role in the bipolar memristive behaviors since oxygen vacancies can directly determine the local conductivity in many systems. However, a recent theoretical work demonstrated that both ... More

A quantum gravity tensor equation formally integrating general relativity with quantum mechanicsJun 09 2016Extending black-hole entropy to ordinary objects, we propose kinetic entropy tensor, based on which a quantum gravity tensor equation is established. Our investigation results indicate that if N=1, the quantum gravity tensor equation returns to Schrodinger ... More

On the Borel transgression in the fibration $G\rightarrow G/T$Oct 09 2017Let $G$ be a semisimple Lie group with a maximal torus $T$. We present an explicit formula for the Borel transgression $\tau :H^{1}(T)\rightarrow H^{2}(G/T)$ of the fibration $G\rightarrow G/T$. This formula corrects an error in the paper \cite{K}, and ... More

On the inverse Kostka matrixJun 13 2003We present both a combinatorial characterization and a recurrent formula for the entries of the inverse Kostka matrix. An application to the topology of the classifying space BU(n) is obtained.

Collective neutrino oscillations and spontaneous symmetry breakingJun 29 2015Neutrino oscillations in a hot and dense astrophysical environment such as a core-collapse supernova pose a challenging, seven-dimensional flavor transport problem. To make the problem even more difficult (and interesting), neutrinos can experience collective ... More

Two elliptic closed geodesics on positively curved Finsler spheresApr 01 2015Jul 10 2015In this paper, we prove that for every Finsler $n$-dimensional sphere $(S^{n},F)$ with reversibility $\lm$ and flag curvature $K$ satisfying $\left(\frac{\lm}{1+\lm}\right)^2<K\le 1$, either there exist infinitely many closed geodesics, or there exist ... More

A.C.I.M for Random Intermittent Maps : Existence, Uniqueness and Stochastic StabilityDec 08 2011Jul 24 2012We study a random map $T$ which consists of intermittent maps $\{T_{k}\}_{k=1}^{K}$ and a position dependent probability distribution $\{p_{k,\varepsilon}(x)\}_{k=1}^{K}$. We prove existence of a unique absolutely continuous invariant measure (ACIM) for ... More

Schubert calculus and cohomology of Lie groups. Part II. Compact Lie groupsFeb 02 2015Apr 15 2016Let $G$ be a compact Lie group with a maximal torus $T$. Based on a presentation of the integral cohomology ring $H^{\ast}(G/T)$ of the flag manifold $G/T$ in \cite{DZ1}we have presented in \cite{DZ2}an explicit and unified construction of the integral ... More

The characteristic classes and Weyl invariants of Spinor groupsOct 09 2018Feb 22 2019Based on a pair of cohomology operations on so called $\delta-2$-formal spaces, we construct the integral cohomology rings of the classifying spaces of the Lie groups $Spin(n)$ and $Spin^{c}(n)$. As applications, we introduce characteristic classes for ... More

Fast MPEG-CDVS Encoder with GPU-CPU Hybrid ComputingMay 27 2017Jun 09 2017The compact descriptors for visual search (CDVS) standard from ISO/IEC moving pictures experts group (MPEG) has succeeded in enabling the interoperability for efficient and effective image retrieval by standardizing the bitstream syntax of compact feature ... More

Generating Giant and Tunable Nonlinearity in a Macroscopic Mechanical Resonator from Chemical Bonding ForceJun 24 2015Nonlinearity in macroscopic mechanical system plays a crucial role in a wide variety of applications, including signal transduction and processing, synchronization, and building logical devices. However, it is difficult to generate nonlinearity due to ... More

Dynamic Modulation of the Transport Properties of the LaAlO3/SrTiO3 Interface Using Uniaxial StrainJul 11 2016Among the interfacial transport modulations to the LaAlO3/SrTiO3 (LAO/STO) heterostructure, mechanical strain has been proven to be an effective approach by growing the LAO/STO films on different substrates with varying lattice mismatches to STO. However, ... More

Hyperbolicity of the time-like extremal surfaces in minkowski spacesJun 15 2017In this paper, it is established, in the case of graphs, that time-like extremal surfaces of dimension $1+n$ in the Minkowski space of dimension $1+n+m$ can be described by a symmetric hyperbolic system of PDEs with the very simple structure (reminiscent ... More

Galois action on the Neron-Severi group of Dwork surfacesSep 23 2018Oct 23 2018We study the Galois action attached to the Dwrok surfaces $X_{\lambda}:X_0^4+X_1^4+X_2^4+X_3^4-4\lambda X_0X_1X_2X_3=0$ with parameter $\lambda$ in a number field $F$. We show that when $X_{\lambda}$ has geometric Picard number $19$, its N\'eron-Severi ... More

Prolific interaction structures and shape-changing collisions in an erbium-doped fiber systemJan 13 2016Jan 20 2016Prolific interactions of nonlinear waves on a plane-wave background in an erbium-doped fiber system are unveiled, based on explicit coexistence conditions extracting from the general higher-order solution of a coupled nonlinear Schr\"odinger and the Maxwell-Bloch ... More

Three-Dimensional Fermi-Surface and Electron-Phonon Coupling in Semimetallic 1T-TiTe2 studied by Angle-Resolved Photoemission SpectroscopyAug 31 2018We present an investigation on electronic structure of 1T-TiTe2 material via high-resolution angle-resolved photoemission spectroscopy (ARPES), utilizing tunable photon energy excitations. The typical semimetal-like electronic structure is observed and ... More

Energy loss of charm quarks from $J/ψ$ production in cold nuclear matterDec 15 2013$J/\psi$ suppression in p-A collisions is studied by considering the nuclear effects on parton distribution, energy loss of beam proton and the finial state energy loss of color octet $c\overline{c}$. The leading-order computations for $J/\psi$ production ... More

Improved Sufficient Conditions for Exact Convex Relaxation of Storage-Concerned EDMar 25 2016To avoid simultaneous charging and discharging of storages, complementarity constraints are introduced to storage-concerned economic dispatch (ED), which makes the problem non-convex. This letter concerns the conditions under which the convex relaxation ... More

Quantum Information Meets Quantum Matter -- From Quantum Entanglement to Topological Phase in Many-Body SystemsAug 11 2015May 22 2016This is the draft version of a textbook, which aims to introduce the quantum information science viewpoints on condensed matter physics to graduate students in physics (or interested researchers). We keep the writing in a self-consistent way, requiring ... More

Adaptive Low-Nonnegative-Rank Approximation for State Aggregation of Markov ChainsOct 14 2018This paper develops a low-nonnegative-rank approximation method to identify the state aggregation structure of a finite-state Markov chain under an assumption that the state space can be mapped into a handful of meta-states. The number of meta-states ... More

Surface symmetry breaking and disorder effects on superconductivity in perovskite BaBi3 epitaxial filmsAug 22 2018The structural or electronic symmetry breaking of the host lattice is a recurrent phenomenon in many quantum materials, including superconductors. Yet, how these broken symmetry states affect the electronic pair wave function of superconductivity have ... More

Transfer Metric Learning: Algorithms, Applications and OutlooksOct 09 2018Nov 12 2018Distance metric learning (DML) aims to find an appropriate way to reveal the underlying data relationship. It is critical in many machine learning, pattern recognition and data mining algorithms, and usually require large amount of label information (such ... More

Quantum Discriminant Analysis for Dimensionality Reduction and ClassificationOct 01 2015Jul 08 2016We present quantum algorithms to efficiently perform discriminant analysis for dimensionality reduction and classification over an exponentially large input data set. Compared with the best-known classical algorithms, the quantum algorithms show an exponential ... More

Entangling many atomic ensembles through laser manipulationJan 28 2002Apr 24 2002We propose an experimentally feasible scheme to generate Greenberger-Horne-Zeilinger (GHZ) type of maximal entanglement between many atomic ensembles based on laser manipulation and single-photon detection. The scheme, with inherent fault tolerance to ... More

Quantum Metrology with Dicke Squeezed StatesJun 30 2014Jul 02 2014We introduce a new class of quantum many-particle entangled states, called the Dicke squeezed (or DS) states, which can be used to improve the precision in quantum metrology beyond the standard quantum limit. We show that the enhancement in measurement ... More

A new way of detecting intergalactic baryonsJan 02 2013Jan 20 2013For each photon wave packet of extragalactic light, the dispersion by line-of-sight intergalactic plasma causes an increase in the envelope width and a chirp (drift) in the carrier frequency. It is shown that for continuous emission of many temporally ... More

Efficient classical simulation of noisy quantum computationOct 07 2018Understanding the boundary between classical simulatability and the power of quantum computation is a fascinating topic. Direct simulation of noisy quantum computation requires solving an open quantum many-body system, which is very costly. Here, we develop ... More

Fast Deployment of UAV Networks for Optimal Wireless CoverageOct 16 2017May 15 2018Unmanned Aerial Vehicle (UAV) networks have emerged as a promising technique to rapidly provide wireless coverage to a geographical area, where a flying UAV can be fast deployed to serve as cell site. Existing work on UAV-enabled wireless networks overlook ... More

A Review of Mathematical Modeling, Simulation and Analysis of Membrane Channel Charge TransportSep 29 2016The molecular mechanism of ion channel gating and substrate modulation is elusive for many voltage gated ion channels, such as eukaryotic sodium ones. The understanding of channel functions is a pressing issue in molecular biophysics and biology. Mathematical ... More

A Multiplicative Ergodic Theorem for Discontinuous Random Dynamical Systems and ApplicationsApr 23 2012Jan 07 2018Motivated by studying stochastic systems with non-Gaussian L\'evy noise, spectral properties for a type of linear cocycles are considered. These linear cocycles have countable jump discontinuities in time. A multiplicative ergodic theorem is proved for ... More

Finding Semi-Analytic Solutions of Power System Differential-Algebraic Equations for Fast Transient Stability SimulationDec 02 2014Feb 08 2017This paper studies the semi-analytic solution (SAS) of a power system's differential-algebraic equation. A SAS is a closed-form function of symbolic variables including time, the initial state and the parameters on system operating conditions, and hence ... More

Economics of Age of Information Management under Network ExternalitiesApr 03 2019Apr 10 2019Online content platforms concern about the freshness of their content updates to their end customers, and increasingly more platforms now invite and pay the crowd to share real-time information (e.g., news and sensor data) to help reduce their ages of ... More

A geometric $q$-character formula for snake modulesMay 13 2019Let $\mathscr{C}$ be the category of finite dimensional modules over the quantum affine algebra $U_q(\widehat{\mathfrak{g}})$ of a simple complex Lie algebra ${\mathfrak{g}}$. Let $\mathscr{C}^-$ be the subcategory introduced by Hernandez and Leclerc. ... More

A Stochastic Approach for Parameterizing Unresolved Scales in a System with MemoryJan 21 2009Complex systems display variability over a broad range of spatial and temporal scales. Some scales are unresolved due to computational limitations. The impact of these unresolved scales on the resolved scales needs to be parameterized or taken into account. ... More

Large deviations for the Boussinesq Equations under Random InfluencesFeb 10 2008Nov 07 2008A Boussinesq model for the Benard convection under random influences is considered as a system of stochastic partial differential equations. This is a coupled system of stochastic Navier-Stokes equations and the transport equation for temperature. Large ... More

A hierarchical random compression method for kernel matricesMar 13 2018In this paper, we propose a hierarchical random compression method (HRCM) for kernel matrices in fast kernel summations. The HRCM combines the hierarchical framework of the H-matrix and a randomized sampling technique of the column and row spaces for ... More

Band-gap bowing and p-type doping of (Zn, Mg, Be)O wide-gap semiconductor alloys: a first-principles studyNov 28 2009Using a first-principles band-structure method and a special quasirandom structure (SQS) approach, we systematically calculate the band gap bowing parameters and \emph{p}-type doping properties of (Zn, Mg, Be)O related random ternary and quaternary alloys. ... More

Entanglement detection in the vicinity of arbitrary Dicke statesJul 26 2011Dicke states represent a class of multipartite entangled states that can be generated experimentally with many applications in quantum information. We propose a method to experimentally detect genuine multipartite entanglement in the vicinity of arbitrary ... More

Scaling Ion Trap Quantum Computation through Fast Quantum GatesJan 29 2004We propose a method to achieve scalable quantum computation based on fast quantum gates on an array of trapped ions, without the requirement of ion shuttling. Conditional quantum gates are obtained for any neighboring ions through spin-dependent acceleration ... More

General Hubbard model for strongly interacting fermions in an optical lattice and its phase detectionJun 14 2007Based on consideration of the system symmetry and its Hilbert space, we show that strongly interacting fermions in an optical lattice or superlattice can be generically described by a lattice resonance Hamiltonian. The latter can be mapped to a general ... More

Dynamic Pricing and Capacity Allocation of UAV-provided Mobile ServicesDec 07 2018Due to its agility and mobility, the unmanned aerial vehicle (UAV) is a promising technology to provide high-quality mobile services (e.g., fast Internet access, edge computing, and local caching) to ground users. Major Internet Service Providers (ISPs) ... More

Coverless information hiding based on Generative ModelFeb 10 2018A new coverless image information hiding method based on generative model is proposed, we feed the secret image to the generative model database, and generate a meaning-normal and independent image different from the secret image, then, the generated ... More

Statistical analysis of the limitation of half integer resonances on the available momentum acceptance of a diffraction-limited storage ringJun 23 2016In a diffraction-limited storage ring (DLSR), the momentum acceptance (MA) might be limited by the half integer resonances (HIRs) excited by focusing errors, associated with the large detuning terms from the strong focusing and strong sextupoles required ... More

A unified formula for Steenrod operations in flag manifoldsJun 17 2003Feb 14 2005The classical Schubert cells on a flag manifold G/H give a cell decomposition for G/H whose Kronecker duals (known as Schubert classes) form an additive base for the integral cohomology H^{\ast}(G/H). We present a formula that expresses Steenrod mod-p ... More

High-order accurate entropy stable finite difference schemes for one- and two-dimensional special relativistic hydrodynamicsMay 15 2019This paper develops the high-order accurate entropy stable finite difference schemes for one- and two-dimensional special relativistic hydrodynamic equations. The schemes are built on the entropy conservative flux and the weighted essentially non-oscillatory ... More

Schubert calculus and the Hopf algebra structures of exceptional Lie groupsMar 26 2009Aug 29 2010Let G be an exceptional Lie group with a maximal torus T. Based on common properties in the Schubert presentation of the cohomology ring H*(G/T;F_{p}) DZ1, and concrete expressions of generalized Weyl invariants for G over F_{p}, we obtain a unified approach ... More

Schubert presentation of the integral cohomology ring of the flag manifolds G/TJan 16 2008Feb 08 2015Let G be a compact connected Lie group with a maximal torus T\subsetG. In the context of Schubert calculus we obtain a canonical presentation for the integral cohomology ring H^{\ast}(G/T) of the complete flag manifold G/T. The result have been applied ... More

Schubert calculus and cohomology of Lie groups. Part I. 1-connected Lie groupsNov 16 2007Sep 10 2015Let $G$ be a compact and $1$--connected Lie group with a maximal torus $T$. Based on Schubert calculus on the flag manifold $G/T$ [15] we construct the integral cohomology ring $H^{\ast}(G)$ uniformly for all $G$.

The Chow rings of generalized GrassmanniansNov 14 2005Aug 08 2008Based on the Basis theorem of Bruhat--Chevalley [C] and the formula for multiplying Schubert classes obtained in [D\QTR{group}{u}] and programed in [DZ$_{\QTR{group}{1}}$], we introduce a new method computing the Chow rings of flag varieties (resp. the ... More

Algorithm for multiplying Schubert classesSep 09 2003Oct 22 2005Based on the multiplicative rule of Schubert classes obtained in [Du3], we present an algorithm computing the product of two arbitrary Schubert classes. As a result, the algorithm gives also a method to compute the integral cohomology ring of a flag manifold ... More

Quantifying Uncertainties in Complex SystemsDec 01 2009Jul 20 2010Uncertainties are abundant in complex systems. Mathematical models for these systems thus contain random effects or noises. The models are often in the form of stochastic differential equations, with some parameters to be determined by observations. The ... More

Impacts of Noise on a Class of Partial Differential EquationsFeb 25 2014Oct 11 2014This paper is concerned with effects of noise on the solutions of partial differential equations. We first provide a sufficient condition to ensure the existence of a unique positive solution for a class of stochastic parabolic equations. Then, we prove ... More

Separation between quantum Lovász number and entanglement-assisted zero-error classical capacityAug 16 2016Quantum Lov\'asz number, as a natural generalization of the celebrated Lov\'asz number in graph theory, is the best known efficiently computable upper bound of the entanglement-assisted zero-error classical capacity of a quantum channel. However, it remains ... More

The Boltzmann Equation with Large-amplitude Initial Data in Bounded DomainsMar 23 2017Nov 13 2018The paper is devoted to constructing the global solutions around global Maxwellians to the initial-boundary value problem on the Boltzmann equation in general bounded domains with isothermal diffuse reflection boundaries. We allow a class of non-negative ... More

Martingale and Weak Solutions for a Stochastic Nonlocal Burgers Equation on Bounded IntervalsOct 28 2014This work is about the existence of martingale solutions and weak solutions for a stochastic nonlocal Burgers equation on bounded intervals. The existence of a martingale solution is shown by using a Galerkin approximation, Prokhorov's theorem and Skorokhod's ... More

Second Order Cone Constrained Convex Relaxations for Nonconvex Quadratically Constrained Quadratic ProgrammingAug 06 2016Sep 16 2017In this paper, we present new convex relaxations for nonconvex quadratically constrained quadratic programming (QCQP) problems. While recent research has focused on strengthening convex relaxations using reformulation-linearization technique (RLT), the ... More

Multiple closed geodesics on bumpy Finsler $n$-spheresMay 30 2007In this paper we prove that for every bumpy Finsler metric $F$ on every rationally homological $n$-dimensional sphere $S^n$ with $n\ge 2$, there exist always at least two distinct prime closed geodesics.

Economics of Age of Information Management under Network ExternalitiesApr 03 2019Apr 04 2019Online content platforms concern about the freshness of their content updates to their end customers, and increasingly more platforms now invite and pay the crowd to share real-time information (e.g., news and sensor data) to help reduce their ages of ... More

Flavor instabilities in the neutrino line modelDec 22 2014May 28 2015A dense neutrino medium can experience collective flavor oscillations through nonlinear neutrino-neutrino refraction. To make this multi-dimensional flavor transport problem more tractable, all existing studies have assumed certain symmetries (e.g., the ... More

On the multiplicity of closed geodesics on Finsler spheres with irrationally elliptic closed geodesicsApr 27 2015If all prime closed geodesics on $(S^n,F)$ with an irreversible Finsler metric $F$ are irrationally elliptic, there exist either exactly $2\left[\frac{n+1}{2}\right]$ or infinitely many distinct closed geodesics. As an application, we show the existence ... More

A linear-time algorithm for generalized trust region problemsJul 19 2018In this paper, we provide the first provable linear-time (in the number of non-zero entries of the input) algorithm for approximately solving the generalized trust region subproblem (GTRS) of minimizing a quadratic function over a quadratic constraint ... More

SO(4) Monopole As A New Topological Invariant And Its Topological StructureNov 10 1998By making use of the decomposition theory of gauge potential, the inner structure of SU(2) and SO(4) gauge theory is discussed in detail. We find the SO(4) monopole can be given via projecting the SO(4) gauge field onto an antisymmetric tensor. This projection ... More

Dependence Structure Analysis Of Meta-level Metrics in YouTube Videos: A Vine Copula ApproachDec 29 2017This paper uses vine copula to analyze the multivariate statistical dependence in a massive YouTube dataset consisting of 6 million videos over 25 thousand channels. Specifically we study the statistical dependency of 7 YouTube meta-level metrics: view ... More

State space decomposition for nonautonomous dynamical systemsMar 26 2009Decomposition of state spaces into dynamically different components is helpful for the understanding of dynamical behaviors of complex systems. A Conley type decomposition theorem is proved for nonautonomous dynamical systems defined on a non-compact ... More

Appendix to "The Chow rings of generalized Grassmannians"Oct 05 2005Nov 21 2007In this appendix we tabulate preliminary data used in establishing Theorem 1-14 in the paper ``The Chow rings of generalized Grassmannians''

Harmonic field in knotted spaceApr 26 2018Knotted fields enrich a variety of physical phenomena, ranging from fluid flows, electromagnetic fields, to textures of ordered media. Maxwell's electrostatic equations, whose vacuum solution is mathematically known as a harmonic field, provide an ideal ... More

Asymptotic methods for stochastic dynamical systems with small non-Gaussian Lévy noiseJan 04 2012Feb 17 2014The goal of the paper is to analytically examine escape probabilities for dynamical systems driven by symmetric $\alpha$-stable L\'evy motions. Since escape probabilities are solutions of a type of integro-differential equations (i.e., differential equations ... More

On the non-degeneracy of radial vortex solutions for a coupled Ginzburg-Landau systemMay 01 2019For the following Ginzburg-Landau system in ${\mathbb R}^2$ \begin{align*} \begin{cases} -\Delta w^+ +\Big[A_+\big(|w^+|^2-{t^+}^2\big)+B\big(|w^-|^2-{t^-}^2\big)\Big]w^+=0, \\[3mm] -\Delta w^- +\Big[A_-\big(|w^-|^2-{t^-}^2\big)+B\big(|w^+|^2-{t^+}^2\big)\Big]w^-=0, ... More

Optimal deployment of sustainable UAV networks for providing wireless coverageMar 27 2019Each UAV is constrained in its energy storage and wireless coverage, and it consumes most energy when flying to the top of the target area, leaving limited leftover energy for hovering at its deployed position and providing wireless coverage. The literature ... More

Ergodicity of Stochastically Forced Large Scale Geophysical FlowsApr 12 2001We investigate the ergodicity of 2D large scale quasigeostrophic flows under random wind forcing. We show that the quasigeostrophic flows are ergodic under suitable conditions on the random forcing and on the fluid domain, and under no restrictions on ... More

Constructing Infinitely Many Geometric Triangulations Of The Figure Eight Knot ComplementAug 20 2015This paper considers "geometric" ideal triangulations of cusped hyperbolic 3-manifolds, i.e. decompositions into positive volume ideal hyperbolic tetrahedra. We exhibit infinitely many geometric ideal triangulations of the figure eight knot complement. ... More

Local distinguishability of orthogonal 2\otimes3 pure statesSep 11 2007Oct 08 2007We present a complete characterization for the local distinguishability of orthogonal $2\otimes 3$ pure states except for some special cases of three states. Interestingly, we find there is a large class of four or three states that are indistinguishable ... More

Topology of Blow-ups and Enumerative GeometryJun 23 2009Sep 04 2016Let M be the blow--up of a manifold M along a submanifold X. In this paper we present closed formulae for the integral cohomology and the total Chern class of M. As applications we compute the cohomology of the varieties of complete conics and complete ... More

A parameter estimation method based on random slow manifoldsMar 19 2013A parameter estimation method is devised for a slow-fast stochastic dynamical system, where often only the slow component is observable. By using the observations only on the slow component, the system parameters are estimated by working on the slow system ... More

Controlling ultracold atoms in multi-band optical lattices for simulation of Kondo physicsOct 16 2003We show that ultracold atoms can be controlled in multi-band optical lattices through spatially periodic Raman pulses for investigation of a class of strongly correlated physics related to the Kondo problem. The underlying dynamics of this system is described ... More

Does light from steady sources bear any observable imprint of the dispersive intergalactic medium?Nov 29 2017There has recently been some interest in the prospect of detecting ionized intergalactic baryons by examining the properties of incoherent light from background cosmological sources, namely quasars. Although the paper by \cite{lieu13} proposed a way forward, ... More

An impact of stochastic dynamic boundary conditions on the evolution of the Cahn-Hilliard systemAug 04 2006Nonlinear systems are often subject to random influences. Sometimes the noise enters the system through physical boundaries and this leads to stochastic dynamic boundary conditions. A dynamic, as opposed to static, boundary condition involves the time ... More